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Flowfield modeling and diagnostics
Flowfield Modeling and Diagnostics. D. G. LILLEY. Abacus L39.75
Press, Tunbridge
By A. K. G UPTA and Wells,
1985,414
pp.,
The Abacus’ series on “Energy and Engineering Sciences”, edited by Gupta and Lilley, offers nine titles of which seven relate to combustion and three are authored by the editors themselves. The jacket notes tell us that Gupta and Lilley hold faculty appointments in the States but started out as graduate researchers in the U.K., at Sheffield University where they undoubtedly trained with J. Swithenbank’s group to judge from the ground covered in this text. In a nutshell, it contains about 30 pages of introductory generalities, about 140 pages on calculation methods (the “modeling”), about 140 pages on measurement methods (the “diagnostics”), and about 80 pages on largely unresolved problems in the prediction and suppression of pollution. As an overall opinion from one who came to this book knowing a little about the fluid mechanics side but not so much about combustion and its production of pollutants, I would say their treatment of turbulent flow modelling is unnecessarily and misleadingly oversimplified, whilst the coupled thermo-kinetic-dynamics of combustion certainly offer a daunting challenge for secure progress beyond the semi-empirical fix-ups that are presently employed. The 30-page introduction provides a thumbnail sketch of the authors’ pragmatic attitude to the development of “flowfield” analyses for turbulent transport and combustion: essentially that ReynoldssBoussinesq model equations are to be adopted, without further ado, for confined swirl jet flows and their transport of combusting reactants in axisymmetric geometries. The practical context is briefly illustrated by reference to classification schemes for flames and burning strategies in engines and furnaces. Finally, there are a few comments on the computational and experimental tools which they advocate: for the former, primitive variable discretisation of the model equations, in particular the TEACH code [now elderly (1974)). but updates are available; for the latter, non-intrusive optical methods, e.g. laser flow anemometry and particle sizing are recommended against probe-supported sensors, despite uncertainties about refractive distortions. Breaking down their 140 pages on calculation methods, we find about 40 pages are given to turbulent flow modelling, about 40 pages to combustion/pollution modelling, about 30 pages to scaling arguments/integral estimates and about 30 pages to numerical schemes for local estimates. Right from the outset, Gupta and Lilley adopt Boussinesq’s gradient-flux field formulation for the undetermined Reynolds terms, without questioning its validity restriction, strictly, to quasiequilibrium turbulence-in Townsend’s sense of gradually varied mean field forcing. This sweeping assumption hardly seems appropriate for the rapidly reciprocating flows of piston engines, or the abrupt expansion/centerbody flows of turbine engines. Putting these doubts to one side, the eddy diffusivity closure is then effected via one-point macroscale parameterisation of the turbulence, modified empirically for swirl inhibition and patched to assumed equilibrium “logarithmic” wall zones, i.e. effective fully-turbulent boundary conditions. As expected, the authors broadly discount algebraic closure of the mean field equations. e.g. Prandtl’s mixing length model, and specifically advocate differential closure in terms of a two-parameter transport equation model for turbulence
kinetic energy and dissipation rate: the famous “k--E” model, for which infamous supplementary constants must be assigned empirically to the eddy coefficient ratios, i.e. an “eddy Prandtl number” for each of the Reynolds terms in the mean field and model turbulence equations. Eddy field closure, expressed via additional model transport equations for all of the Reynolds terms appearing in the mean field equations, is sensibly discouraged because “optimising the constants” is too formidable and because the resulting codes are computationally intensive. Similar sentiments are reasonably expressed about eddy structure modelling and large eddy simulation approaches, which are also impracticable for direct applications to complex engineering flows. Cautious encouragement is rightly shown for more tractable direct extensions of the one-point macroscale approach to threeparameter transport equation modelling, with eddy shear stress supplementing k and E, and to so-called algebraic eddy stress modelling which offers a first estimate of partitioning between the stress components when the advective and diffusive fluxes are neglected. As an introductory overview of engineering calculation methods, their account falls short of the mark particularly with regard to its lack of any emphatic cautions about the strictly limited empirical status that attaches to the closure schemes adopted in all these one-point transport models of the Reynolds-averaged equations. Whilst the differential closures may be of practical value as extended data correlations, i.e. convenient computational “black-boxes” and versatile, too, with several adjustable constants available for “optimisation”, it really should be made absolutely clear that no special fundamental status is conferred on the models simply because they are formulated in terms of local rate equations for the turbulence parameters. Indeed, there are no guarantees of gaining broader validity by introducing additional parameter transport equations, i.e. going from the k--E model to eddy stress modelling, because this route also introduces new uncertainties about approximate representations of the eddy structural integrals associated with distortional modulation and isotropisingdrift due to pressure straining, i.e. the socalled rapid and Rotta modelling terms. For a simple qualitative illustration of the physical limitation of these approaches, consider that Boussinesq closure implies that there is always a localised and instantaneous response of the eddy flux to the assumed driving gradient of Now this quasiReynolds-averaged quantity. each equilibrium statistical approximation usually suffices for most molecular transport processes because the relaxation scales, e.g. of the impulse response function, are usually negligible compared with any of the continuum scales of the mean and eddy fields. On the other hand, the same consideration certainly does not hold for transport by the energetic eddies of most turbulent shear flows, where the macroscale eddy sizes and memories, as parameterised by k and E, are often comparable with the mean field scales. Consequently. macroscale Boussinesq closure really should not be trusted to furnish a physically adequate description in these circumstances. However, if it is imposed, then the closure coefficients must be expected to display some dependence on the eddy deformational history, manifested as transit memory integrals sensitive to both the boundary configuration and initial condition of the flow. Indeed, there is solid experimental evidence that, even in the ideal classical case of a plane free shear, or mixing, layer between parallel unconfined coflowing streams, the eddy Prandtl number for scalar spread-
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Press, Tunbridge
By A. K. G UPTA and Wells,
1985,414
pp.,
The Abacus’ series on “Energy and Engineering Sciences”, edited by Gupta and Lilley, offers nine titles of which seven relate to combustion and three are authored by the editors themselves. The jacket notes tell us that Gupta and Lilley hold faculty appointments in the States but started out as graduate researchers in the U.K., at Sheffield University where they undoubtedly trained with J. Swithenbank’s group to judge from the ground covered in this text. In a nutshell, it contains about 30 pages of introductory generalities, about 140 pages on calculation methods (the “modeling”), about 140 pages on measurement methods (the “diagnostics”), and about 80 pages on largely unresolved problems in the prediction and suppression of pollution. As an overall opinion from one who came to this book knowing a little about the fluid mechanics side but not so much about combustion and its production of pollutants, I would say their treatment of turbulent flow modelling is unnecessarily and misleadingly oversimplified, whilst the coupled thermo-kinetic-dynamics of combustion certainly offer a daunting challenge for secure progress beyond the semi-empirical fix-ups that are presently employed. The 30-page introduction provides a thumbnail sketch of the authors’ pragmatic attitude to the development of “flowfield” analyses for turbulent transport and combustion: essentially that ReynoldssBoussinesq model equations are to be adopted, without further ado, for confined swirl jet flows and their transport of combusting reactants in axisymmetric geometries. The practical context is briefly illustrated by reference to classification schemes for flames and burning strategies in engines and furnaces. Finally, there are a few comments on the computational and experimental tools which they advocate: for the former, primitive variable discretisation of the model equations, in particular the TEACH code [now elderly (1974)). but updates are available; for the latter, non-intrusive optical methods, e.g. laser flow anemometry and particle sizing are recommended against probe-supported sensors, despite uncertainties about refractive distortions. Breaking down their 140 pages on calculation methods, we find about 40 pages are given to turbulent flow modelling, about 40 pages to combustion/pollution modelling, about 30 pages to scaling arguments/integral estimates and about 30 pages to numerical schemes for local estimates. Right from the outset, Gupta and Lilley adopt Boussinesq’s gradient-flux field formulation for the undetermined Reynolds terms, without questioning its validity restriction, strictly, to quasiequilibrium turbulence-in Townsend’s sense of gradually varied mean field forcing. This sweeping assumption hardly seems appropriate for the rapidly reciprocating flows of piston engines, or the abrupt expansion/centerbody flows of turbine engines. Putting these doubts to one side, the eddy diffusivity closure is then effected via one-point macroscale parameterisation of the turbulence, modified empirically for swirl inhibition and patched to assumed equilibrium “logarithmic” wall zones, i.e. effective fully-turbulent boundary conditions. As expected, the authors broadly discount algebraic closure of the mean field equations. e.g. Prandtl’s mixing length model, and specifically advocate differential closure in terms of a two-parameter transport equation model for turbulence
kinetic energy and dissipation rate: the famous “k--E” model, for which infamous supplementary constants must be assigned empirically to the eddy coefficient ratios, i.e. an “eddy Prandtl number” for each of the Reynolds terms in the mean field and model turbulence equations. Eddy field closure, expressed via additional model transport equations for all of the Reynolds terms appearing in the mean field equations, is sensibly discouraged because “optimising the constants” is too formidable and because the resulting codes are computationally intensive. Similar sentiments are reasonably expressed about eddy structure modelling and large eddy simulation approaches, which are also impracticable for direct applications to complex engineering flows. Cautious encouragement is rightly shown for more tractable direct extensions of the one-point macroscale approach to threeparameter transport equation modelling, with eddy shear stress supplementing k and E, and to so-called algebraic eddy stress modelling which offers a first estimate of partitioning between the stress components when the advective and diffusive fluxes are neglected. As an introductory overview of engineering calculation methods, their account falls short of the mark particularly with regard to its lack of any emphatic cautions about the strictly limited empirical status that attaches to the closure schemes adopted in all these one-point transport models of the Reynolds-averaged equations. Whilst the differential closures may be of practical value as extended data correlations, i.e. convenient computational “black-boxes” and versatile, too, with several adjustable constants available for “optimisation”, it really should be made absolutely clear that no special fundamental status is conferred on the models simply because they are formulated in terms of local rate equations for the turbulence parameters. Indeed, there are no guarantees of gaining broader validity by introducing additional parameter transport equations, i.e. going from the k--E model to eddy stress modelling, because this route also introduces new uncertainties about approximate representations of the eddy structural integrals associated with distortional modulation and isotropisingdrift due to pressure straining, i.e. the socalled rapid and Rotta modelling terms. For a simple qualitative illustration of the physical limitation of these approaches, consider that Boussinesq closure implies that there is always a localised and instantaneous response of the eddy flux to the assumed driving gradient of Now this quasiReynolds-averaged quantity. each equilibrium statistical approximation usually suffices for most molecular transport processes because the relaxation scales, e.g. of the impulse response function, are usually negligible compared with any of the continuum scales of the mean and eddy fields. On the other hand, the same consideration certainly does not hold for transport by the energetic eddies of most turbulent shear flows, where the macroscale eddy sizes and memories, as parameterised by k and E, are often comparable with the mean field scales. Consequently. macroscale Boussinesq closure really should not be trusted to furnish a physically adequate description in these circumstances. However, if it is imposed, then the closure coefficients must be expected to display some dependence on the eddy deformational history, manifested as transit memory integrals sensitive to both the boundary configuration and initial condition of the flow. Indeed, there is solid experimental evidence that, even in the ideal classical case of a plane free shear, or mixing, layer between parallel unconfined coflowing streams, the eddy Prandtl number for scalar spread-
1215